.
i1 : R = ZZ/101[x]
o1 = R
o1 : PolynomialRing
|
i2 : M = R^4
4
o2 = R
o2 : R-module, free
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i3 : A = random(M,M)
o3 = | 50 38 -40 -40 |
| 10 27 -6 14 |
| -36 47 32 -37 |
| -49 21 37 -16 |
4 4
o3 : Matrix R <--- R
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i4 : factor det(x*id_M - A)
3 2
o4 = (x + 44)(x - 36x + 19x - 33)
o4 : Expression of class Product
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i5 : (B,P,Q) = rationalNormalForm A
o5 = (| 1 0 0 0 |, | 18 21 20 20 |, | 50 -17 47 -18 |)
| 0 36 1 0 | | 5 -11 -34 -50 | | -2 -37 49 1 |
| 0 -19 0 1 | | -2 -36 -30 -31 | | 16 45 -12 0 |
| 0 33 0 0 | | 12 15 -33 30 | | 39 -6 -6 0 |
o5 : Sequence
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i6 : B - P*A*Q == 0
o6 = true
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i7 : P*Q - id_M == 0
o7 = false
|